Simona Halep’s Match Points

Italian translation at settesei.it

In the second-set tiebreak of Sunday’s Cincinnati final, Simona Halep reached match point against Kiki Bertens. She failed to convert, then Bertens claimed the tiebreak, and the third set–and the championship–went the way of the Dutchwoman. It was a bit of painful deja vu for Halep fans, who watched the top-ranked player reach match point against Su Wei Hsieh at Wimbledon only to miss her chance and crash out in the third round.

Halep has a reputation as a bit of a weak closer–not just match points, but set points and, more generally, service games with the set or match on the line. Her overall ability to finish matches is beyond the scope of a single post, but we can start by biting off the smaller chunk of, specifically, her performance on match points, and how that compares to the rest of the WTA.

Let’s start with the basics. For everyone, reaching match point is (obviously!) a really good sign that she’ll go on to win the match. Across about 16,000 WTA matches since 2011 for which I have sequential point-by-point data, players who hold match point end up winning the match a bit more than 97% of the time. That doesn’t mean that they convert on the first try, or even in the game or set of their first opportunity, but even when conversion is elusive, players manage to generate more chances until they finish the job.

If Simona really is a weak closer, we’ll need to look elsewhere for evidence. In the matches for which I possess the point-by-point sequence*, there are 251 contests in which Halep held a match point, stretching between the end of 2011 and this month’s Rogers Cup in Montreal. Of those, she eventually converted a match point 250 times. That is, with the exception of the Wimbledon match against Hsieh, she didn’t lose any matches in which she was a point away from victory.

* I don’t have the point-by-point sequence for every Halep match, but I have most of them, and the missing ones are random. The same applies to just about every WTA player. Some of the raw data is available here; I’m hoping to update with 2017 and 2018 data in the near future.

Compared to the best players, this level of MP conversion doesn’t even stand out. Among the 50 women with at least 100 matches in which they held match point, five–Serena Williams, Victoria Azarenka, Andrea Petkovic, Ekaterina Makarova, and Elena Vesnina—always converted, if not always on the first try. (Again, I’m missing some matches, but that doesn’t take away from the fact that in a random sample of 259 matches, Serena remains perfect.) Until Sunday’s Cincinnati final, Halep was one of eight more–with Petra Kvitova, Maria Sharapova, and Ana Ivanovic, among others–who failed to convert only once.

Situational performance

It’s no accident that the most dominating names in tennis are near the top of that list. Yes, the best players are most likely to win at match point, but just as important, the best players are more likely to earn several opportunities. Deep in a tiebreak, one missed chance can represent the final hope, but most of the time when Halep, Serena, or someone else of their ilk fails to convert an opportunity, they’re still leading by, say, a set and a break, making it easy to generate more chances.

That leads us to another question: How do players perform on match point itself? Does the pressure lead to fewer points won, compared to non-MP serve and return points? Or do other factors, like momentum or crowd support, cause players to do even better when one point away from victory?

It turns out that there’s no single answer; the results are a bit different depending on whether the player holding match point is serving or returning. When a player is serving to finish off a match, she is slightly less likely to win the point, compared to her serve performance up to that point. It’s not a big difference–a bit less than a 3% drop in the rate of serve points won–but it is persistent across several years of WTA results. When players are one point away from victory but are returning, there is no match-point effect. They win return points at the same rate regardless of whether a handshake is imminent.

Match points are almost evenly distributed between serve and return points–on the WTA tour, about 55% are serve points, leaving 45% return points. Thus, given the 3% drop on serve performance and the lack of change on return points, players win approximately 1.5% fewer points when one step away from victory than otherwise. One player who almost exactly parallels the average is Caroline Wozniacki–in 271 match-point matches and 474 match points, she won those MPs at a rate 1.7% lower than non-MPs.

Some of the players who almost always win their match-point matches aren’t any better than average when we look at individual points. For instance, Sharapova wins MPs a rate 1.2% lower than non-MPs, and Azarenka’s success rate drops by 1.4%. Dominika Cibulkova won 198 of the 201 match-point matches in my dataset despite her success rate falling by a whopping seven percent.

Halep, however, doesn’t fit in that category. In her 251 match-point matches, she has held 420 individual match points, which she has won at a rate 4.4% higher than her non-MP rates in the same set of matches. Few players are better, though a handful are overwhelmingly so, such as Kvitova at +9.0%, and Vesnina at +13.9%. The vast majority of women are within a few percentage points of neutral: They win match points, whether serve or return, about as often as they win non-match-points.

Random results

These numbers tell us only one thing: what has happened in the past. It is tempting to use them to make predictions, or perhaps lay down a sizable wager the next time Vesnina is a point away from victory. But when most players are so close to neutral, it’s a warning that much of what we’re looking at may be random.

If players have consistent tendencies in match point situations, we would be able to identify that in the data. For instance, we might see that Kvitova converts match points at a high rate in each individual season. Since the single-season totals make for sometimes small samples, I took a slightly different approach. For players with at least 60 match-point matches, I randomly divided their matches into two separate groups, and determined how their performance at MP compared to their success rate on other points. Again, if this were a real skill, we would expect that players would be roughly the same in each of their two random groups–better than usual on MP in both groups, or worse.

Alas, for this population of 80 players with sufficient match-point samples, there is no correlation at all. If women have consistent, predictable tendencies to outperform or underperform in match-point opportunities, these inclinations are either extremely small, or they don’t persist over several years.

This is a familiar refrain when looking at specific situations in tennis matches. Our hyperactive, pattern-seeking brains find it easy to identify apparent tendencies, but in general, players win points at about the same rate regardless of the context. Over the medium term, like the half-decade represented by my point-by-point dataset, some players will stick out, like Kvitova, Vesnina, and to a lesser extent, Halep. But past results are hardly a guarantee of future match-point performance. The smart prediction for any player’s upcoming results on match point is that she’ll do exactly as well as she does the rest of the time. It’s a rather boring conclusion. Thankfully, the match points situations themselves are usually exciting enough on their own.

Economist: The new serve clock in tennis appears to be backfiring

At the Economist Game Theory blog, I wrote about the early effects of the new serve clock. The outwardly stricter time policy didn’t speed up Rafael Nadal, nor did it cut down match times in general over its first two weeks:

The Toronto champion wasn’t the only player who slowed down once on the clock. At each of the completed tournaments where the serve clock has been used—Toronto, Montreal, San Jose, and Washington, D.C.—the average point took longer in 2018 than it did in 2017, without the clock. The differences varied from 0.3 seconds per point at the women’s event San Jose (an event that was held in nearby Stanford last year) to 2.0 seconds at the men’s competition in Washington.

Read the whole thing.

Dominating Your Countrymen

This is a guest post by Peter Wetz.

Italian translation at settesei.it

When Andy Murray lost to fellow Brit Kyle Edmund at the 2018 Eastbourne International, The Sunday Times headlined that this was Andy’s first loss to a countryman in twelve years. Indeed, twelve years is a long time, and not too many readers will remember his round of 32 loss against Tim Henman in 2006 at the Thailand Open.

However, if you don’t play often against players from your country, twelve years may feel much shorter. Indeed, between his losses in 2006 and 2018 Andy only played and won four matches against other Britons. From October 2006 to June 2016 there was not even a single match Andy had to play against one of his countrymen. Out of the five matches since his loss in 2006, he won four. Doesn’t look that impressive anymore.

So who are the players that really dominated foes holding the passport? First, let’s look at the longest winning streaks in terms of matches. The list shows players who amassed at least a 10-match winning streak against players from their country, since 1991. Matches that were not completed due to retirements or walkovers are ignored.

Player		Start		End		Matches
Pete Sampras	1993-03		1994-05		34
Pete Sampras	1995-12		1997-02		23
Rafael Nadal	2004-08		2005-10		22
Sergi Bruguera	1993-09		1995-07		20
Rafael Nadal	2008-05		2010-05		19
Sergi Bruguera	1992-04		1993-07		19
Andy Roddick	2006-07		2009-08		18
Guillermo Coria	2002-08		2004-05		18
Stefan Edberg	1991-07		1994-02		18
Andre Agassi	2000-01		2001-08		17
James Blake	2006-02		2007-07		16
Juan C. Ferrero	2002-09		2004-04		16
Rafael Nadal	2012-05		2013-10		15
Carlos Moya	2004-01		2005-01		15
Tomas Berdych	2006-06		2017-01		14*
John Isner	2013-04		2014-07		13
Rafael Nadal	2011-03		2012-04		13
Roger Federer	2009-08		2013-03		13
Andre Agassi	2004-08		2006-03		12
Juan C. Ferrero	2000-02		2001-04		12
Magnus Larsson	1996-04		1999-08		12
Rafael Nadal	2016-02		2018-04		11*
David Ferrer	2011-07		2012-04		11
Novak Djokovic	2008-06		2011-11		11
Andy Roddick	2003-06		2004-03		11
R. Schuettler	2000-08		2003-08		11
Lleyton Hewitt	1999-06		2001-05		11
Y. Kafelnikov	1995-03		2000-10		11
Carlos Costa	1993-07		1994-04		11
Renzo Furlan	1991-03		1994-08		11

* Active streaks of active players

Three players, Pete Sampras, Rafael Nadal and Sergi Bruguera, each with multiple entries, stick out on top of the list. Coming from countries that are known for regularly having players at the top of the rankings, these streaks look even more impressive. Obviously, Pete Sampras, for instance, often got the opportunity to play against other Americans. Hence, when he was at the peak of his career, he could pile up wins for his streak count over a short amount of time–as long as he kept defeating formidable opponents such as Andre Agassi, Jim Courier, and Michael Chang.

What if we relax the number of matches contributing to the streak and take a look at the temporal duration of a streak? The list shows all winning streaks against players from the same country lasting 36 months or longer and consisting of four or more matches. The third column shows the duration of the streak in months, the fourth column shows how many matches per month were played during the streak–to give an indication of how regularly the player faced a fellow–and the last column shows how many matches contribute to the streak.

Player		Start		Dur	M/Mon	Matches
Tomas Berdych	2006-06		127	0.11	14*
Jurgen Melzer	2003-07		87	0.07	6
Juan MD Potro	2009-02		85	0.08	7
Thomas Muster	1991-06		83	0.12	10
Tim Henman	1999-03		74	0.09	7
Novak Djokovic	2012-06		70	0.07	5*
Roger Federer	2000-05		69	0.12	8
Milos Raonic	2012-05		69	0.06	4
Y. Kafelnikov	1995-03		67	0.16	11
Lleyton Hewitt	2009-02		65	0.09	6
David Goffin	2012-01		63	0.06	4*
F. Volandri	2003-09		58	0.1	6
Dominik Hrbaty	2000-10		57	0.07	4
Kevin Kim	2000-08		53	0.08	4
Lleyton Hewitt	2001-11		51	0.08	4
Steve Darcis	2008-06		50	0.1	5
A. Chesnokov	1991-04		47	0.11	5
Gustavo Kuerten	1997-04		46	0.11	5
R. Krajicek	1992-06		44	0.23	10
Roger Federer	2009-08		43	0.3	13
Novak Djokovic	2008-06		41	0.27	11
Renzo Furlan	1991-03		41	0.27	11
Magnus Larsson	1996-04		40	0.3	12
Marcos Ondruska	1994-03		40	0.1	4
Andy Roddick	2006-07		36	0.5	18
R. Schuettler	2000-08		36	0.31	11
Tommy Haas	2009-06		36	0.19	7
F. Gonzalez	2006-08		36	0.14	5
H. Zeballos	2014-02		36	0.11	4

* Active streaks of active players

(Andy Murray’s streak is not on this list, because we define the duration of a streak as the time between the first and last match satisfying the condition of the streak, in this case winning matches against countrymen. In his case these dates are June and October 2016 making his streak just short of four months.)

Tomas Berdych comes out on top of the list with a huge gap over the second-place Jurgen Melzer. Berdych’s still active streak of winning against countrymen started more than twelve years ago (the duration of the streak is not exactly that long, because currently the streak stops at his last completed match win which was against Jiri Vesely in January 2017). The streak currently consists of 14 match wins with a relatively low rate of matches per month (0.11).

All of the players who topped the former list don’t qualify for this one, because their streaks, while spanning large numbers of matches, didn’t last as many years as the latter accomplishments. However, two members of the big four, Roger Federer and Novak Djokovic appear. The case of Roger Federer is special in that since 2005 out of 26 matches, he only faced two different opponents. Of these 26 matches, he faced Stan Wawrinka 24 times and Marco Chiudinelli twice. His streak starting in 2009 essentially represents his head-to-head against Wawrinka over this period of time. Fun fact: David Goffin is the only player from this list who still has a clean sheet and never lost a match against another Belgian on the ATP tour.

Aside from the current streak of Tomas Berdych, the lack of long active streaks shows us that there are no countries where one player has been dominating everyone else over the past few years. Even the top guys occasionally lose when facing an opponent from the same nation. There’s only one way to reliably avoid losing to a countryman: As Marcos Baghdatis, Grigor Dimitrov, or Kevin Anderson can tell you, the trick is to hail from a nation with no other top-level competition at all.

—

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Podcast Episode 29: A New Davis Cup and a Career Golden Masters

In Episode 29 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, we spend so much time talking about the Davis Cup reforms, if ITF head David Haggerty were to listen, he’d immediately try to change our format to something shorter. While we recorded the episode before yesterday’s finals in Cincinnati, we also touch on several other topics: the impressiveness of Novak Djokovic’s career record at all the Masters, the players who–like Sloane Stephens–have powerful groundstrokes that they save for special occasions, and Simona Halep’s aggressive scheduling.

Thanks for listening!

(Note: this week’s episode is about 66 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Update: Episode index with links, thanks to FBITennis:

Davis Cup Reforms Generally 1:49
Team and mixed gender tennis trend 6:15
Effect of DC reforms on smaller tennis federations 8:11
Will big stars play more often in the new DC format? 12:17
Davis Cup analogy to World Baseball Classic 18:39
Which countries benefit most from the new DC format? 22:09
Cincinnati F (men’s):  Djokovic v Federer 26:05
US Open favorites (men’s) 29:45
How close is Stan Wawrinka in getting back to form? 33:12
Variation in ground stroke speed (e.g., Wawrinka, Stephens) 37:10
Simona Halep’s crazy schedule 47:05
Discussion of New Haven event 50:26
US Open qualifying matches (how to choose?) 57:00

Measuring a Season’s Worth of Luck

In Toronto last week, Stefanos Tsitsipas was either very clutch, very lucky, or both. Against Alexander Zverev in Friday’s quarter-final, he won fewer than half of all points, claiming only 56.7% of his service points, compared to Zverev’s 61.2%. The next day, beating Kevin Anderson in the semi-final in a third-set tiebreak, he again failed to win half of total points, holding 69.9% of his service points against Anderson’s 75.5%.

Whether the Greek prospect played his best on the big points or benefited from a hefty dose of fortune, this isn’t sustainable. Running those serve- and return-points-won (SPW and RPW) numbers through my win probability model, we find that–if you take luck and clutch performance out of the mix–Tsitsipas had a 27.8% chance of beating Zverev and a 26.5% chance of beating Anderson. These two contests–perhaps the two days that have defined the youngster’s career up to this point–are the very definition of “lottery matches.” They could’ve gone either way, and over a long enough period of time, they’ll probably even out.

Or will they? Are some players more likely to come out on top in these tight matches? Are they consistently–dare I say it–clutch? Using this relatively simple approach of converting single-match SPW and RPW rates into win probabilities, we can determine which players are winning more or less often than they “should,” and whether it’s a skill that some players consistently display.

Odds in the lottery

Let’s start with some examples. When one player wins more than 55% of points, he is virtually guaranteed to win the match. Even at 53%, his chances are extremely good. Still, a lot of matches–particularly best-of-threes on fast surfaces–end up in the range between 50% and 53%, and that’s what most interesting from this perspective.

Here are Tsitsipas’s last 16 matches, along with his SPW and RPW rates and the implied win probability for each:

Tournament  Round  Result  Opponent     SPW    RPW  WinProb  
Toronto     F      L       Nadal      62.9%  21.1%       3%  
Toronto     SF     W       Anderson   69.9%  24.5%      27%  
Toronto     QF     W       A Zverev   56.7%  38.8%      28%  
Toronto     R16    W       Djokovic   77.2%  32.0%      85%  
Toronto     R32    W       Thiem      83.3%  30.2%      93%  
Toronto     R64    W       Dzumhur    82.8%  35.0%      98%  
Washington  SF     L       A Zverev   54.7%  25.5%       1%  
Washington  QF     W       Goffin     71.2%  32.7%      67%  
Washington  R16    W       Duckworth  80.0%  37.5%      98%  
Washington  R32    W       Donaldson  59.5%  45.5%      74%  
Wimbledon   R16    L       Isner      72.5%  18.0%      10%  
Wimbledon   R32    W       Fabbiano   64.0%  55.9%     100%  
Wimbledon   R64    W       Donaldson  70.1%  40.9%      95%  
Wimbledon   R128   W       Barrere    71.5%  39.0%      94%  
Halle       R16    L       Kudla      59.7%  28.8%       8%  
Halle       R32    W       Pouille    78.3%  42.9%      99%

More than half of the matches are at least 90% or no more than 10%. But that leaves plenty of room for luck in the remaining matches. Thanks in large part to his last two victories, the win probability numbers add up to only 9.8 wins, compared to his actual record of 12-4. All four losses were rather one-sided, but in addition to the Toronto matches against Zverev and Anderson, his wins against David Goffin in Washington and, to a lesser extent, Novak Djokovic in Toronto, were far from sure things.

In the last two months, Stefanos has indeed been quite clutch, or quite lucky.

Season-wide views

When we expand our perspective to the entire 2018 season, however, the story changes a bit. In 48 tour-level matches through last week’s play (excluding retirements), Tsitsipas has gone 29-19. The same win probability algorithm indicates that he “should” have won 27.4 matches–a difference of 1.6 matches, or about five percent, which is less than the gap we saw in his last 16. In other words, for the first two-thirds of the season, his results were either unlucky or un-clutch, if only slightly. At the very least, the aggregate season numbers are less dramatic than his recent four-event run.

For two-thirds of a season, a five percent gap between actual wins and win-probability “expected” wins isn’t that big. For players with at least 30 completed tour-level matches this season, the magnitude of the clutch/luck effect extends from a 20% bonus (for Pierre Hugues Herbert) to a 20% penalty (for Sam Querrey, which he reduced a bit by beating John Isner in Cincinnati on Monday despite winning less than 49% of total points). Here are the ten extremes at each end, of the 59 ATPers who have reached the threshold so far in 2018:

Player                 Matches  Wins  Exp Wins  Ratio  
Pierre Hugues Herbert       30    16      13.2   1.22  
Nikoloz Basilashvili        34    17      14.0   1.21  
Frances Tiafoe              39    24      20.0   1.20  
Evgeny Donskoy              30    13      10.9   1.19  
Grigor Dimitrov             34    20      17.1   1.17  
Lucas Pouille               31    16      13.7   1.17  
Gael Monfils                34    21      18.3   1.15  
Daniil Medvedev             34    18      15.8   1.14  
Marco Cecchinato            33    19      16.7   1.14  
Maximilian Marterer         32    17      15.2   1.12  
…                                                      
Leonardo Mayer              37    19      20.1   0.95  
Guido Pella                 37    20      21.2   0.95  
Marin Cilic                 38    27      28.8   0.94  
Novak Djokovic              37    27      29.3   0.92  
Marton Fucsovics            30    16      17.5   0.92  
Joao Sousa                  36    18      19.8   0.91  
Dusan Lajovic               34    17      18.7   0.91  
Fernando Verdasco           43    22      24.5   0.90  
Mischa Zverev               39    18      20.7   0.87  
Sam Querrey                 30    15      18.8   0.80

A difference of three or four wins, as many of these players display between their actual and expected win totals, is more than enough to affect their standing in the rankings. The degree to which it matters depends enormously on which matches they win or lose, as Tsitsipas’s semi-final defeat of Anderson has a much greater impact on his point total than, say, Querrey’s narrow victory over Isner does for his. But in general, the guys at the top of this list are ones who have seen unexpected ranking boosts this season, while some of the guys at the bottom have gone the other way.

The last full season

Let’s take a look at an entire season’s worth of results. Last year, a few players–minimum 40 completed tour-level matches–managed at least a 20% luck/clutch bonus, but with the surprising exception of Daniil Medvedev, none of them have repeated the feat so far in 2018:

Player                 Matches  Wins  Exp Wins  Ratio  
Donald Young                43    21      16.2   1.30  
Fabio Fognini               58    35      28.5   1.23  
Jack Sock                   55    36      29.8   1.21  
Jiri Vesely                 45    22      19.3   1.14  
Daniil Medvedev             43    22      19.7   1.11  
John Isner                  57    36      32.3   1.11  
Damir Dzumhur               56    33      29.7   1.11  
Gilles Muller               48    30      27.1   1.11  
Alexander Zverev            74    53      48.1   1.10  
Juan Martin del Potro       53    37      33.6   1.10

A few of these players have had solid seasons, but posting a good luck/clutch number in 2017 is hardly a guaranteed, as the likes of Donald Young, Jack Sock, and Jiri Vesely can attest. Here is the same list, with 2018 luck/clutch ratios shown alongside last year’s figures:

Player                 2017 Ratio  2018 Ratio     
Donald Young                 1.30        0.89  *  
Fabio Fognini                1.23         1.1     
Jack Sock                    1.21        0.68  *  
Jiri Vesely                  1.14        1.08  *  
Daniil Medvedev              1.11        1.14     
John Isner                   1.11        0.96     
Damir Dzumhur                1.11        1.01     
Gilles Muller                1.11        0.84  *  
Alexander Zverev             1.10        1.06     
Juan Martin del Potro        1.10        1.07

* fewer than 30 completed tour-level matches

The average luck/clutch ratio of these ten players has fallen to a bit below 1.0.

Unsustainable luck

You can probably see where this is going. I generated full-season numbers for each year from 2008 to 2017, and identified those players who appeared in the lists for adjacent pairs of seasons. If luck/clutch ratio is a skill–that is, if it’s more clutch than luck–guys who post good numbers will tend to do so the following year, and those who post lower numbers will be more likely to remain low.

Across 325 pairs of player-seasons, that’s not what happened. There is almost no relationship between one year of luck/clutch ratio and the next. The r^2 value–a measure of correlation–is 0.07, meaning that the year-to-year numbers are close to random.

Across sports, analysts have found plenty of similar results, and they are often quick to pronounce that “clutch doesn’t exist,” which leads to predictable rejoinders from the laity that “of course it does,” and so on. It’s boring, and I’m not particularly interested in that debate. What this specific finding shows is:

This type of luck, defined as winning more matches than implied by a player’s SPW and RPW in each match, is not sustainable.

What Tsitsipas accomplished last weekend in Toronto was “clutch” by almost any definition. What this finding demonstrates is that a few such performances–or even a season’s worth of them–doesn’t make it any more likely that he’ll do the same next year. Or, another possibility is that the players who stick at the top level of professional tennis are all clutch in this sense, so while Tsitsipas might be quite mentally strong in key moments, he’ll often run up against players who have similar mental skills, and he won’t be able to consistently win these close matches.

If Stefanos is able to maintain a ranking in the top 20, which seems plausible, he’ll probably need to win more serve and return points than he has so far. Fortunately for him, he’s still almost eight years younger than his typical peer, so he has plenty of time to improve. The occasional lottery matches that tilt his way will need to be mere bonuses, not the linchpin of his strategy to reach the top.

Podcast Episode 28: Tsitsipas, Sloane, and the Serve Clock

Episode 28 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, is our triumphant (re-) return to podcasting. We cover all the highlights from last week’s Rogers Cup, especially the breakout week from Stefanos Tsitsipas, the strong showing from Sloane Stephens, and the quiet dominance of Rafael Nadal and Simona Halep.

We also cover tennis’s new serve clock, which has entered the game surprisingly smoothly … but without much effect on the pace of play. Thanks for listening!

(Note: this week’s episode is about 63 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Update: Episode index with links, thanks to FBITennis:

Tsitsipas in Toronto 1:17
Performance Byes [pp 45-46 in linked pdf] 8:05
Next Gen One-Handed Backhands 13:29
Sloane Stephens’ Ranking Profile 19:38
Effectiveness of Kamau Murray 27:40
Do the Canadian Results Affect US Open Favorites? 33:00
Dimitrov defending in Cincinnati 37:30
Federer returns in Cincinnati 40:55
Muguruza defending in Cincinnati 45:06
Average Age of ATP Top 50 Declining 48:30
Serve Clock 52:34

Maybe, Finally, The Next Generation is Here

Italian translation at settesei.it

Alexander Zverev is winning Masters titles. Stefanos Tsitsipas is beating top ten players. Denis Shapovalov, Frances Tiafoe, and even Alex De Minaur are making life more difficult for ATP veterans.

For most of the last decade, the story of men’s tennis has been the degree to which the game is getting older. Even now, thirty-somethings hold half of the places in the top ten. Wave after wave of hyped prospects have failed to take over the sport, settling in for a long fight to the top.  On Monday, Juan Martin del Potro, once hailed as the man who would topple the Big Four, will reach a new career-best ranking of No. 3 … six weeks away from his 30th birthday.

At last, though, men’s tennis appears to be getting younger. Teenagers Shapovalov, Tiafoe, and De Minaur are rising just as some of the game’s crustiest vets are on their way out: 36-year-olds David Ferrer and Julien Benneteau are calling it quits this year, tumbling in the rankings alongside the likes of Feliciano Lopez and Ivo Karlovic.

The result is that the average age of the ATP top 50 is falling–something it hasn’t done for a really, really long time. The following graph shows the average age of the top 50 at the end of every season since 1983, plus–the rightmost data point–the mean age of the current top 50:

At the end of 2017, the average age was 29.0 years; it has since fallen to 27.75. That’s bigger than any single-year swing (up or down) in the last 35 years. As the graph shows, there were plenty of “down” years in the late 1990s and early 2000s, but none of them had even half the magnitude of the current drop.

There’s still an enormous gap between the current state of affairs and the days when men’s tennis was young. If we expand our view to the top 100, this year’s shift is less dramatic–with Ferrer, Benneteau, Lopez and others ranked between 51 and 100, that average still sits at 28.1 years, only about seven months younger than the corresponding number at the end of last season. But even that weaker evidence of a youth movement points in the same direction: 28.1 years is the youngest the top 100 has been since 2012.

Barring fundamental changes in rules or equipment, we’re unlikely to return to the teenage-driven game of the early 1990s. But after a decade of waiting, watching, and wondering, we can see some cracks in the greatest generation of men’s tennis. And finally, there’s a group of young players ready to take advantage.

The Cost of a Double Fault

We all know that double faults aren’t good, but it’s less clear just how bad they are. Over the course of an entire match, a single point here or there doesn’t seem to matter too much, especially when a double fault creeps in at a harmless moment, like 40-love. Yet many missed second serves are far more costly. Let’s try to quantify the impact of tennis’s most enervating outcome.

To do this, we need to think in terms of win probability. In each match, a player wins a certain percentage of service points and a certain percentage of return points. If those rates are sufficiently dominating–say, Mihaela Buzarnescu’s 65% of service points won and 59% of return points won in last week’s San Jose final–the player’s chance of winning the match is 100%. No matter how unlucky or unclutch she was, those percentages result in a win. But in a close contest, in which both players win about 50% of points (often referred to as “lottery matches”), the result is heavily influenced by clutch play and luck. In Buzarnescu’s tour de force, flipping the result of a single point would be meaningless. But in a tight match, like the Wimbledon semifinal between John Isner and Kevin Anderson, a single point could mean the difference between a spot in the championship match and an early flight home.

My aim, then, is to measure the average win probability impact of a double fault. To take another example, consider last week’s Washington quarter-final between Andrea Petkovic and Belinda Bencic. Bencic won nearly 51% of total points–59% of her service points and 42% on return–but lost in a third-set tiebreak. Those serve and return components were enough to give her a 56.3% chance of winning the match: claiming more than half of total points usually results in victory, but so close to 50%, there’s plenty of room for things to go the other way.

I refer to this match because double faults played a huge role. Bencic tallied 12 double faults in 105 service points, a rate of 11.4%, more than double the WTA tour average of 5.1%. Had she avoided those 12 double faults and won those points at the same rate as her other 93 service points, she would have ended up with a much more impressive service-points-won rate of 67%. Combined with her 42% rate of return points won, that implies an 87% chance of winning the match–more than 30 percentage points higher than her actual figure! Roughly speaking, each of her 12 double faults cost her a 2.5% chance (30% divided by 12) of winning the match.

A double fault rate above 10% is unusual, but a cost of 2.5% per offense is not. When we run this algorithm across the breadth of the ATP and WTA tours, we find that the cost of double faults adds up fast.

Tour averages

Using the method I’ve described above–replacing double faults with average non-double-fault service points–and taking the average of all tour-level matches in 2017 and 2018 through last week’s tournaments, we find that the average WTA double fault costs a player 1.83% of a win. Put another way, every 55 additional double faults subtracts one match from the win column and adds one to the loss column.

In the men’s game, the equivalent number is 1.99% of a win. The slightly bigger figure is due to the fact that men, on average, win more service points, so the difference between a double fault and a successful service offering is greater.

There is, however, an alternative way we could approach this. By comparing double faults to all other service points, we’re trading a lot of the double faults for first serve outcomes. We might be more interested in knowing how a player would fare if his or her second serve were bulletproof–still eliminating double faults, but replacing them specifically with second serves instead of a generic mix of service points.

In that case, the algorithm remains very similar. Instead of replacing double faults with non-double-fault serve points, we replace them with non-double-fault second serve points. Then the cost of a double fault is a little bit less, because second serve points result in fewer points won than service points overall. The second-serve numbers are 1.61% per double fault in the women’s game and 1.70% per double fault in the men’s game. For the remainder of this post, I’ll stick with the generic service points, but one approach is not necessarily better than the other; they simply measure different things.

Building a player-specific stat

Odious as double faults are, they are not completely avoidable. Very few players are able to sustain a double fault rate below 2%, and tour averages are around twice that. Since the beginning of 2017, the ATP average has been about 3.9%, and the WTA average roughly 5.1%, as we saw above.

We can measure players by considering their match-by-match double fault rates compared to tour average. In Bencic’s unfortunate case, her 12 double faults were 6.7 more than a typical player would’ve committed in the same number of service points. In contrast, in the same match, Petkovic recorded only 3 double faults in 102 service points, 2.2 double faults fewer than an average player would have.

We know that each WTA double fault affects a player’s chances of winning the match by 1.83%, so compared to an average service performance, Bencic’s excessive service errors cost her about a 17% chance of winning (6.7 times 1.83%), while Petkovic’s stinginess increased her own odds by about 6.6% (2.2 times 1.83%).

Repeat the process for every one of a player’s matches, and you can assemble a longer-term statistic. Let’s start with the WTA players who, since the start of last season, have cost themselves the most matches (“DF Cost”–negative numbers are bad), along with those who have most improved their lot by avoiding double faults:

Player                   DF%  DF Cost  
Kristina Mladenovic     7.7%    -3.84  
Daria Gavrilova         7.9%    -3.77  
Jelena Ostapenko        7.7%    -3.58  
Petra Kvitova           8.1%    -3.01  
Camila Giorgi           8.3%    -2.63  
Oceane Dodin           10.2%    -2.51  
Donna Vekic             7.0%    -1.91  
Venus Williams          6.7%    -1.71  
Coco Vandeweghe         6.4%    -1.60  
Aliaksandra Sasnovich   6.7%    -1.55  
…                                      
Agnieszka Radwanska     2.3%     1.27  
Sloane Stephens         2.1%     1.43  
Caroline Wozniacki      3.2%     1.43  
Barbora Strycova        3.5%     1.47  
Elina Svitolina         3.9%     1.48  
Simona Halep            3.5%     1.53  
Qiang Wang              2.6%     1.54  
Anastasija Sevastova    3.1%     1.57  
Carla Suarez Navarro    2.1%     1.67  
Caroline Garcia         3.6%     1.82

And the same for the men:

Player                  DF%  DF Cost  
Benoit Paire           6.2%    -4.51  
Ivo Karlovic           5.8%    -3.63  
Fabio Fognini          5.0%    -2.38  
Denis Shapovalov       6.3%    -2.26  
Grigor Dimitrov        5.1%    -2.25  
Gael Monfils           5.0%    -2.22  
David Ferrer           5.2%    -2.06  
Jeremy Chardy          5.3%    -2.00  
Fernando Verdasco      4.8%    -1.94  
Jack Sock              4.8%    -1.73  
…                                     
Roger Federer          2.1%     0.88  
Tomas Berdych          2.9%     0.89  
Juan Martin del Potro  2.8%     0.93  
Albert Ramos           3.1%     0.97  
Pablo Carreno Busta    2.2%     1.07  
Richard Gasquet        2.6%     1.12  
John Isner             2.6%     1.23  
Dusan Lajovic          1.9%     1.23  
Denis Istomin          1.9%     1.23  
Philipp Kohlschreiber  2.5%     1.24

Situational double faults

These aggregate numbers have the potential to hide a lot of information. They consider only two things about each match: how many double faults a player committed, and how close the match was. This statistic would treat Bencic the same whether she hit nine of her double faults at 40-love, or nine of her double faults in the third-set tiebreak. Yet the latter would have a colossally greater impact.

While this is an important limitation to keep in mind, it appears that double faults are distributed relatively randomly. That is, most players do not hit a majority of their double faults in particularly high- or low-leverage situations. The player lists displayed above show both the most basic stat–double fault percentage–along with my more complex approach. For players with at least 20 matches since the beginning of last season, double fault rate is very highly correlated with the match-denominated cost of double faults. (For men, r^2 = 0.752, and for women, r^2 = 0.789.) In other words, most of the variance in double fault cost can be explained by the number of double faults, leaving little room for other factors, such as the importance of the situation when double faults are committed.

That said, there’s plenty of room for additional analysis into those specific sitations. Instead of taking a match-level look at win probability, as I have here, one could identify the point score of every single one of a player’s double faults, and see how each event affected the win probability of that match. I suspect that, for most players, that would amount to a whole lot of extra complexity for not a lot of added insight, but perhaps there are some players who are uniquely able to land their second serve when it matters most, or particularly prone to double faults at key moments. This match-level look has made it clear how costly double faults can be, and it’s possible that for some players, missed serves are even more damaging than that.

How Servers Respond To Double Faults

Italian translation at settesei.it

In the professional game, double faults are quite rare. They sometimes reflect a momentary lapse in concentration, and can negatively impact a server’s confidence. Players are sometimes particularly careful after losing a point to a double fault, taking some speed off their next delivery, or aiming closer to the middle of the box.

Let’s dig into some data from last year’s grand slams to see what players do–and how it affects their results–immediately after double faults. IBM’s Slamtracker provided point-by-point data for most 2017 grand slam singles matches, including serve speed and direction, and the available matches give us about 5,000 double faults to work with. (I’ve organized the data and made it freely available here.)

For each server in each match, I’ve tallied their results on points immediately following double faults. (That means that we exclude after-double-fault points when the double fault ended the game.) Then, for each player, I compared those results with match-long averages. Because double faults are so unusual, and because we only have this data for the majors, the sample isn’t adequate to tell us much about individual players. But for tour-wide analyses, it’s more than enough.

Serve points won: As we’ll see in a moment, men and women have different overall tendencies on the point following a double fault. But by the most important measure of simply winning the next point, gender plays little part. Men, who in this sample win 65.1% of service points, fall just over one percentage point to 64.0% on the point following a double fault. Women, who average 57.8% of service points won, drop even more, to 56.1% after a double.

First serve percentage: I expected that servers become more conservative immediately after a double fault. For women, that hypothesis is correct: In these matches, they land 63.3% of their first serves, while after a double fault, that number jumps to 65.4%. On the other hand, men don’t seem to change their approach very much. On average, they make 62.3% of their first offerings, a number that barely changes, to 62.5%, after double faults.

First serve points won: Here is additional evidence that women become more conservative after double faults, while men do not. In general, women win 63.7% of their first serve points, but just after a double fault, that number drops to 62.9%. For men, there is a decrease in first serve points won, but it is almost as small as their difference in first serve percentage: 72.7% overall, 72.4% after a double fault.

First serve speed: With serve speed, we run into a limitation of the Slamtracker data, which gives us speed only for those serves that go in. So when we look at the average speed of first serves, we’re excluding attempts that miss the box. Even with that caveat, the data keeps pointing in the same direction. Contrary to my “conservative” hypothesis, men serve a bit faster than usual after a double fault–183.3 km/h following doubles, versus 182.8 km/h in general. Women do seem to change their tactics, dropping from an average speed of 155.5 km/h to a post-double-fault pace of 152.2 km/h.

First serve direction: Slamtracker divides serve direction into five categories: wide, body-wide, body, body-center, and center. After a double fault, men are less likely than usual to hit a wide serve (24.1% to 25.8%), and those serves get split roughly evenly between the body and center categories. The difference in body serves is most striking: They account for only 3.5% of first serves overall, but 4.4% of post-double first serves. This may be the one way in which men opt for the conservative path, by maintaining speed but giving themselves a wider margin of error.

Women move many of their after-double-fault serves toward the middle of the box. On average, over 44% of serves are classified as either “wide” or “center,” but immediately after a double fault, that number drops below 41%. It’s not a huge difference, but like all of the other tendencies we’ve seen in the women’s game, it suggests that for many players, caution creeps in immediately after missing a second serve.

Tactics

As usual, it’s difficult to move from these sorts of findings to any sort of tactical advice. Even the first data point, that both men and women win fewer service points than usual right after they’ve double faulted, can be interpreted in multiple ways. By one reading, players may be serving too conservatively, missing out of the benefits of big first serves. On the other hand, if confidence is an issue, perhaps serving more aggressively would just result in more misses.

When in doubt, we have to trust that the players and coaches know what they’re doing–they’ve honed these tradeoffs through decades of experience and thousands of hours of match play. For fans, these numbers add to our understanding of the conclusions that players have reached. For the pros, perhaps a more detailed look at what happens after a double fault would help tweak their own strategies, both bouncing back from their own double faults and taking advantage of the lapses in concentration of their opponents.

Men’s Doubles Season Starts and the Case of Oliver Marach and Mate Pavic

This is a guest post by Peter Wetz.

In recent years, the steady decline of the holders of 116 doubles titles–Bob and Mike Bryan–has resulted in more variety at the very top of the game. The 16-time Grand Slam champions won their last major at the US Open 2014. Since then, eight different teams have won their first title at the highest level of the sport.

Even though none of these debut winners emerged out of nowhere, the doubles team consisting of Oliver Marach and Mate Pavic, which formed in the middle of last season, has enjoyed an exceptional run at this year’s start of the season. This prompted me to take a closer look at the performance of doubles teams per season.

The following table shows each team’s won-loss record through the French Open for each season since 2000 . It’s sorted by number of  wins up to that point, and the last column displays the won-loss record for the complete season. Only teams that have won more than 30 matches until the French Open are listed.

Year	Team		W-L (%) Start	W-L (%) Full
2013	Bryan/Bryan	40-4  (91%)	71-11 (87%)
2002	Knowles/Nestor	38-7  (84%)	66-14 (82%)
2007	Bryan/Bryan	37-5  (88%)	73-10 (88%)
2008	Bryan/Bryan	37-9  (80%)	63-17 (79%)
2009	Bryan/Bryan	37-9  (80%)	68-18 (79%)
2014	Bryan/Bryan	36-6  (86%)	64-12 (84%)
2018	Marach/Pavic	36-7  (84%)	tbd
2010	Nestor/Zimonjic	35-7  (83%)	57-19 (75%)
2012	Mirnyi/Nestor	34-9  (79%)	43-18 (70%)
2003	Knowles/Nestor	34-9  (79%)	57-16 (78%)
2006	Bryan/Bryan	33-9  (79%)	65-15 (81%)
2004	Bryan/Bryan	32-8  (80%)	57-17 (77%)
2010	Bryan/Bryan	31-7  (82%)	67-13 (84%)
2011	Bryan/Bryan	31-7  (82%)	59-16 (79%)
2009	Nestor/Zimonjic	31-8  (79%)	57-17 (77%)
2014	Nestor/Zimonjic	31-8  (79%)	42-18 (70%)
2003	Bryan/Bryan	31-12 (72%)	54-20 (73%)

As we can see, Marach/Pavic come in seventh with a very healthy 36-7 won-loss record this year. Their first loss came in the Rotterdam final, their fourth tournament after collecting titles in Doha, Auckland, and at the Australian Open–a streak of 17 consecutive match wins. If we ignore the all-time greats, there hasn’t been a better start to a men’s doubles season in the past 16 years.

The fact that the Bryan twins show up ten out of seventeen times in the table underlines just how dominant they were. And even though they did not win a Grand Slam in the last three years, they still had the best season starts in 2015 and 2016 (just barely missing the table, because they did not reach 30 match wins).

The last column gives a clue of what to expect from Marach and Pavic for the rest of the year. Most of the time, the teams at the very top only slightly decline. Notably, in 2007 the Bryan brothers maintained a win percentage of 88%, which led to the best doubles season in the dataset, measured by won-loss record.

After losing their seventh match this season at the 2018 French Open final to Herbert/Mahut and therefore missing the chance to win the first two majors of the season–a feat achieved in the open era only by the Bryans in 2013–it will be interesting to see if they will be able to sustain their level over a full season.

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Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.